The Mathematics which Simplifies Space Missions

The new NASA space mission program for the next generation of lunar missions is the core of the work by Emanuele Borgonovo (ELEUSI and Department of Decision Sciences) and Curtis Smith (Idaho National Laboratory, USA), A Study of Interactions in the Risk Assessment of Complex Systems: An Application to Space PSA, to appear on Operations Research.

"This article was based upon work sponsored by an agency of the United States government," the usual disclaimer of US government agencies, signals that this is the result of a research project between ELEUSI and the Idaho National Laboratories (INL), one of the main US national labs. The project is part of the Faculty-Staff-Exchange program of INL, which sees Bocconi as the first non-US University in the program for the third consecutive year.

Scientific models play a crucial role in supporting decision-makers in several applications ranging from the modelling of climate change effects to the planning of space missions. It is especially when the decisions at hands involve complex systems and operations that managers need to bring together the varous facets of the problem in a decision-support model. This is, undoubtedly, the case of NASA managers who are planning lunar missions, especially now that they have to select the vehicles, routes, operations, systems (etc.) that will replace the Space Shuttle and insure that the planned mission respects all risk constraints. Thus, it is not surprising that the simulation model describing the mission, from launch, to lunar orbit, lunar landing and return to earth contains more than 400 variables, and a set of around 5000 possible events that can make the mission fail. In this complex framework, interactions play a crucial role. It is likely, in fact, that the variables do not impact mission performance individually. If this is the case, an approach that does not take interactions into account runs the risk of making managers reach misleading conclusions about how to optimize mission performance. However, given 400 variables, one has 2⁴⁰⁰ interactions (that is, billions of billions).

The problem of formulating indicators to be provided to managers that would account for these interactions has been the core of the research project. Borgonovo and Smith have worked on the implementation of a technique developed by Borgonovo (previously published in the European Journal of Operational Research) that makes it possible to synthesize these interactions at a numerical cost of only 800 model runs instead of 2⁴⁰⁰ model runs.

With this result, the method is applicable not only to models for the analysis of space missions, but to several classes of models used in operations research such as, for instance, Bayesian networks.

Through the method, managers obtain several insights as to whether interactions matter in the decision-problem at hand (or if decision-makers are still on the safe side even if ignoring them), and on the identification of the policies that insure that target performance is achieved.